Interactions induced by electromagnetic fluctuations, such as van der Waals and Casimir forces, are of universal nature present at any length scale between any types of systems. Such interactions are important not only for the fundamental science of materials behavior, but also for the design and improvement of micro- and nanostructured devices. In the past decade, many new materials have become available, which has stimulated the need for understanding their dispersive interactions. The field of van der Waals and Casimir forces has experienced an impetus in terms of developing novel theoretical and computational methods to provide new insights into related phenomena. The understanding of such forces has far reaching consequences as it bridges concepts in materials, atomic and molecular physics, condensed-matter physics, high-energy physics, chemistry, and biology. This review summarizes major breakthroughs and emphasizes the common origin of van der Waals and Casimir interactions. Progress related to novel ab initio modeling approaches and their application in various systems, interactions in materials with Dirac-like spectra, force manipulations through nontrivial boundary conditions, and applications of van der Waals forces in organic and biological matter are examined. The outlook of the review is to give the scientific community a materials perspective of van der Waals and Casimir phenomena and stimulate the development of experimental techniques and applications.

In this article we discuss the invariance under general changes of reference frame of all the physical predictions of particle detector models in quantum field theory in general and, in particular, of those used in quantum optics to model atoms interacting with light. We find explicitly how the light-matter interaction Hamiltonians change under general coordinate transformations, and analyze the subtleties of the Hamiltonians commonly used to describe the light-matter interaction when relativistic motion is taken into account.

We theoretically predict that the Casimir force in vacuum between two Chern insulator plates can be repulsive (attractive) at long distances whenever the sign of the Chern numbers characterizing the two plates are opposite (equal). A unique feature of this system is that the sign of the force can be tuned simply by turning over one of the plates or alternatively by electrostatic doping. We calculate and take into account the full optical response of the plates and argue that such repulsion is a general phenomena for these systems as it relies on the quantized zero frequency Hall conductivity. We show that achieving repulsion is possible with thin films of Cr-doped ${(\mathrm{Bi},\mathrm{Sb})}_{2}{\mathrm{Te}}_{3}$, that were recently discovered to be Chern insulators with quantized Hall conductivity.

In this work we study the Casimir effect with three-dimensional topological insulators including the effects of temperature and uniaxial anisotropy. Although precise experimental values for the optical properties of these materials are yet to be established, a qualitative analysis is still possible. We find qualitatively that the reported repulsive behavior and the equilibrium point are robust features of the system, and are favored by low temperatures and the enhancement of the optical response parallel to the optical axis. The dependence of the equilibrium point with temperature and with the topological magnetoelectric polarizability characteristic of three-dimensional topological insulators is also discussed.

The Casimir force is a universal interaction induced by electromagnetic quantum fluctuations between any types of objects. The expansion of the graphene family by adding silicene, germanene and stanene (2D allotropes of Si, Ge, and Sn), lends itself as a platform to probe Dirac-like physics in honeycomb staggered systems in such a ubiquitous interaction. We discover Casimir force phase transitions between these staggered 2D materials induced by the complex interplay between Dirac physics, spin-orbit coupling and externally applied fields. In particular, we find that the interaction energy experiences different power law distance decays, magnitudes and dependences on characteristic physical constants. Furthermore, due to the topological properties of these materials, repulsive and quantized Casimir interactions become possible.

The Casimir interaction, induced by electromagnetic fluctuations between objects, is strongly dependent upon the electronic and optical properties of the materials making up the objects. Here we investigate this ubiquitous interaction between semi-infinite spaces of topologically nontrivial Weyl semimetals. A comprehensive examination of all components of the bulk conductivity tensor and the surface conductivity due to the Fermi arc states in real and imaginary frequency domains is presented using the Kubo formalism for materials with different degree of tilting of their linear energy cones. The Casimir energy is calculated using a generalized Lifshitz approach, for which electromagnetic boundary conditions for anisotropic materials were derived and used. We find that the interaction between Weyl semimetals is metallic-like and its magnitude and characteristic distance dependence can be modified by the degree of tilting and chemical potential. The nontrivial topology plays a secondary role in the interaction and thermal fluctuations are expected to have similar effects as in metallic systems.